The present invention relates generally to cascaded filter banks, and more particularly, to methods and apparatus for reducing the aliasing in such cascaded filter banks.
In signal compression applications, a filter bank with unequal band splitting is often desired to obtain the maximum coding gain. In audio coding applications, for example, band splitting also determines how well the time and frequency shape of the quantization noise after the signal has been decoded is matched to the psycho-acoustic audibility threshold. See, for example, D. Sinha et al., xe2x80x9cThe Perceptual Audio Coder,xe2x80x9d Digital Audio, Section 42, 42-1 to 42-18, (CRC Press, 1998), incorporated by reference herein.
To obtain such unequal band splitting, tree structures are often used. A tree structure may implement, for example, wavelet transforms, such as those described in M. Vetterli and J. Kovacevic, xe2x80x9cWavelets and Subband Coding,xe2x80x9d Prentice Hall (1995), where one or more frequency bands 120, 130, such as the lower frequency band 120, is further split into additional subbands 140-1 through 140-3, as shown in FIG. 1. Other approaches take a uniform filter bank and join several subbands into one wider band to increase bandwidth, such as described in H. S. Malvar, xe2x80x9cLapped Biorthogonal Transforms for Transform Coding with Reduced Blocking and Ringing Artifacts,xe2x80x9d International Conference on Acoustics, Speech, and Signal Processing, Munich, Germany, 2421-2424, (1997). Another approach joins several pieces of different uniform filter banks using transition filters, such as described in J. Princen and J. D. Johnston, xe2x80x9cAudio Coding with Signal Adaptive Filterbanks,xe2x80x9d ICASSP, Detroit, Mich., 3071-3074, (1995).
A cascaded filter bank, such as the cascaded filter bank 100 shown in FIG. 1, has different filter banks 110, 160 following each other to obtain different frequency and time resolutions. The problem with a cascaded filter bank 100 is that the filters are not perfect, and hence the downsampling after each subband filter leads to aliasing. Aliasing occurs when signals with energy outside the filter passband are xe2x80x9cmirroredxe2x80x9d into the passband of the filter.
If this mirrored signal is in the passband of the following filter, the attenuation of the signal is determined only by the first filter of the cascade. This leads to a poor frequency selectivity of the combined filter bank. FIG. 2 displays the magnitude response 200 of a particular band of a filter bank consisting of a cascade with 128 bands in the first stage and 8 bands in the following stage, for a total of 1024 bands, if all subbands of the first stage are split. The aliasing is manifested in the magnitude response 200 as high peaks other than the main lobe, partly with less than 10 dB attenuation. As a comparison, the desired magnitude response 300 can be seen in FIG. 3, which shows a particular band of a 1024 band uniform filter bank.
An approach to reduce this type of aliasing has been incorporated into the MPEG1/Layer 3 audio coder, described in Madisetti and D. B. Williams, eds., xe2x80x9cThe Digital Signal Processing Handbook,xe2x80x9d CRC Press, IEEE Press, Boca Raton, Fla. (1997), incorporated by reference herein. The MPEG-1/Layer 3 audio coder uses a cascaded filter bank, with 32 bands in the first stage and 6 or 18 bands (switchable) in the second stage. For this special type of filter bank, a butterfly like structure is used at the output of the second stage to reduce the aliasing between adjacent bands. See, for example, B. Edler, xe2x80x9cAliasing Reduction in Subbands of Cascaded Filter Banks with Decimation,xe2x80x9d Electronics Letters, Vol. 28, No. 12, pp. 1104-1105, June 1992, incorporated by reference herein.
While the alias reduction techniques incorporated in the MPEG-1/Layer 3 audio coder works for reducing the aliasing in neighboring bands, it only reduces the aliasing from one neighbor, and only in specific filter banks, where the aliasing of neighboring bands has a phase shift of 180 degrees. A need exists for a method and apparatus that reduce aliasing on more than one neighboring band, so that a fixed phase relationship is not required.
Generally, a method and apparatus are disclosed for reducing aliasing between neighboring subbands in cascaded filter banks. According to the present invention, a higher frequency resolution is obtained from a set of subbands. The signals of these subbands are first fed into an alias reduction filter bank to reduce the aliasing. If the first stage filter bank is a modulated uniform filter bank with M1 bands, and the alias reduction filter bank has M2 bands, then to obtain alias cancellation, the alias reduction filter bank has to have the same frequency response as the synthesis filter bank for the first stage, but with the frequency scaled by the ratio of the sampling rates, M1/M2. After the alias reduction filter stage, an analysis filter bank to obtain a higher frequency resolution follows.
According to a further aspect of the invention, a synthesis filter bank for a first stage analysis filter bank can be xe2x80x9cthinned outxe2x80x9d by keeping only every M1/M2th sub-structure. In one disclosed implementation, a two band alias reduction filter is generated from a four band synthesis filter bank with reduced aliasing. The resulting two band filter bank has similar frequency responses (up to the scaling) as the four band filter bank, and hence can be used for the alias reduction.